Electronic properties of interfaces and defects from many-body perturbation theory: Recent developments and applications

We review some recent developments in many body perturbation theory (MBPT) calculations that have enabled the study of interfaces and defects. Starting from the theoretical basis of MBPT, Hedin's equations are presented, leading to the CW and CWI' approximations. We introduce the perturbative approach, that is the one most commonly used for obtaining quasiparticle (QP) energies. The practical strategy presented for dealing with the frequency dependence of the self energy operator is based on either plasmon-pole models (PPM) or the contour deformation technique, with the latter being more accurate. We also discuss the extrapolar method for reducing the number of unoccupied states which need to be included explicity in the calculations. The use of the PAW method in the framework of MBPT is also described. Finally, results which have been obtained using, MBPT for band offsets a interfaces and for defects presented, with companies on the main difficulties and cancels.

Schematic representation of the QP corrections (marked with ) to the band edges (E and E-v) and a defect level (F) for a Si/SiO2 interface (Si and O atoms are represented in blue and red, respectively, in the ball and stick model) with an oxygen vacancy leading to a Si-Si bond (the Si atoms involved in this bond are colored light blue).

A hypercyclic finite rank perturbation of a unitary operator

A unitary operator V and a rank 2 operator R acting on a Hilbert space H are constructed such that V + R is hypercyclic. This answers affirmatively a question of Salas whether a finite rank perturbation of a hyponormal operator can be supercyclic.

Electronic properties of zircon and hafnon from many-body perturbation theory

The electronic properties of zircon and hafnon, two wide-gap high-kappa materials, are investigated using many-body perturbation theory (MBPT) combined with the Wannier interpolation technique. For both materials, the calculated band structures differ from those obtained within density-functional theory and MBPT by (i) a slight displacement of the highest valence-band maximum from the Gamma point and (ii) an opening of the indirect band gap to 7.6 and 8.0 eV for zircon and hafnon, respectively. The introduction of vertex corrections in the many-body self-energy does not modify the results except for a global rigid shift of the many-body corrections.

Density functionals from many-body perturbation theory: The band gap for semiconductors and insulators

Theoretically the Kohn-Sham band gap differs from the exact quasiparticle energy gap by the derivative discontinuity of the exchange-correlation functional. In practice for semiconductors and insulators the band gap calculated within any local or semilocal density approximations underestimates severely the experimental energy gap. On the other hand, calculations with an "exact" exchange potential derived from many-body perturbation theory via the optimized effective potential suggest that improving the exchange-correlation potential approximation can yield a reasonable agreement between the Kohn-Sham band gap and the experimental gap. The results in this work show that this is not the case. In fact, we add to the exact exchange the correlation that corresponds to the dynamical (random phase approximation) screening in the GW approximation. This accurate exchange-correlation potential provides band structures similar to the local density approximation with the corresponding derivative discontinuity that contributes 30%-50% to the energy gap. Our self-consistent results confirm substantially the results for Si and other semiconductors obtained perturbatively [R. W. Godby , Phys. Rev. B 36, 6497 (1987)] and extend the conclusion to LiF and Ar, a wide-gap insulator and a noble-gas solid. (c) 2006 American Institute of Physics.

R-matrix Floquet theory of multiphoton processes:XIII. Resonances in H multiphoton detachment

The results of calculations investigating the effects of autodetaching resonances on the multiphoton detachment spectra of H are presented. The R-matrix Floquet method is used, in which the coupling of the ion with the laser field is described non-perturbatively. The laser field is fixed at an intensity of 10 W cm, while frequency ranges are chosen such that the lowest autodetaching states of the ion are excited through a two- or three-photon transition from the ground state. Detachment rates are compared, where possible, to previous results obtained using perturbation theory. An illustration of how non-lowest-order processes, involving autodetaching states, can lead to light-induced continuum structures is also presented. Finally, it is demonstrated that by using a frequency connecting the 1s and 2s states, the probability of exciting the residual hydrogen atom is significantly enhanced.

Magnetic properties of copper hexadecaphthalocyanine (F16CuPc) thin films and powders

The structural and magnetic properties of F16CuPc thin films and powder, including x-ray diffraction (XRD), superconducting quantum interference device (SQUID) magnetometry, and theoretical modelling of exchange interactions are reported. Analysis of XRD from films, with thickness ranging between 100 and 160 nm, deposited onto Kapton and a perylene-3,4,9,10-tetracarboxylic-3,4,9,10-dianhydride (PTCDA) interlayer shows that the stacking angle (defined in the text) of the film is independent of the thickness, but that the texture is modified by both film thickness and substrate chemistry. The SQUID measurements suggest that all samples are paramagnetic, a result that is confirmed by our theoretical modelling including density functional theory calculations of one-dimensional molecular chains and Green's function perturbation theory calculations for a molecular dimer. By investigating theoretically a range of different geometries, we predict that the maximum possible exchange interaction between F16CuPc molecules is twice as large as that in unfluorinated copper-phthalocyanine (CuPc). This difference arises from the smaller intermolecular spacing in F16CuPc. Our density functional theory calculation for isolated F16CuPc molecule also shows that the energy levels of Kohn-Sham orbitals are rigidly shifted similar to 1 eV lower in F16CuPc compared to CuPc without a significant modification of the intramolecular spin physics, and that therefore the two molecules provide a suitable platform for independently varying magnetism and charge transport. 

Determining the electronic structure and chemical potentials of molecules in solution

A simulation scheme is proposed for determining the excess chemical potential of a substance in solution. First, a Monte Carlo simulation is performed with classical models for solute and solvent molecules. A representative sample of these configurations is then used in a hybrid quantum/classical (QM/MM) calculation, where the solute is treated quantum-mechanically, and the average electronic structure is used to construct an improved classical model. This procedure is iterated to self-consistency in the classical model, which in practice is attained in one or two steps, depending on the quality of the initial guess. The excess free energy of the molecule within the QM/MM approach is determined relative to the classical model using thermodynamic perturbation theory with a cumulant expansion. The procedure provides a method of constructing classical point charge models appropriate for the solution and gives a measure of the importance of solvent fluctuations.

Correlated electron-ion dynamics: the excitation of atomic motion by energetic electrons

Correlated electron-ion dynamics (CEID) is an extension of molecular dynamics that allows us to introduce in a correct manner the exchange of energy between electrons and ions. The formalism is based on a systematic approximation: small amplitude moment expansion. This formalism is extended here to include the explicit quantum spread of the ions and a generalization of the Hartree-Fock approximation for incoherent sums of Slater determinants. We demonstrate that the resultant dynamical equations reproduce analytically the selection rules for inelastic electron-phonon scattering from perturbation theory, which control the mutually driven excitations of the two interacting subsystems. We then use CEID to make direct numerical simulations of inelastic current-voltage spectroscopy in atomic wires, and to exhibit the crossover from ionic cooling to heating as a function of the relative degree of excitation of the electronic and ionic subsystems.

Single-ionization of helium at Ti:sapphire wavelengths: rates and scaling laws

We present a numerical and theoretical study of intense-field single-electron ionization of helium at 390 nm and 780 nm. Accurate ionization rates (over an intensity range of (0.175-34) X10^14 W/ cm^2 at 390 nm, and (0.275 - 14.4) X 10^14 W /cm^2 at 780 nm) are obtained from full-dimensionality integrations of the time-dependent helium-laser Schroedinger equation. We show that the power law of lowest order perturbation theory, modified with a ponderomotive-shifted ionization potential, is capable of modelling the ionization rates over an intensity range that extends up to two orders of magnitude higher than that applicable to perturbation theory alone. Writing the modified perturbation theory in terms of scaled wavelength and intensity variables, we obtain to first approximation a single ionization law for both the 390 nm and 780 nm cases. To model the data in the high intensity limit as well as in the low, a new function is introduced for the rate. This function has, in part, a resemblance to that derived from tunnelling theory but, importantly, retains the correct frequency-dependence and scaling behaviour derived from the perturbative-like models at lower intensities. Comparison with the predictions of classical ADK tunnelling theory confirms that ADK performs poorly in the frequency and intensity domain treated here.

Choline saccharinate and choline acesulfamate: Ionic liquids with low toxicities

Choline saccharinate and choline acesulfamate are two examples of hydrophilic ionic liquids, which can be prepared from easily available starting materials (choline chloride and a non-nutritive sweetener). The (eco)toxicity of these ionic liquids in aqueous solution is very low in comparison to other types of ionic liquids. A general method for the synthesis and purification of hydrophilic ionic liquids is presented. The method consists of a silver-free metathesis reaction, followed by purification of the ionic liquid by ion-exchange chromatography. The crystal structures show a marked difference in hydrogen bonding between the two ionic liquids, although the saccharinate and the acesulfamate anions show structural similarities. The optimized structures, the energetics, and the charge distribution of cation-anion pairs in the ionic liquids were studied by density functional theory (DFT) and second-order (Moller-Plesset) perturbation theory calculations. The occupation of the non-Lewis orbitals was considered to obtain a qualitative picture of the Lewis structures. The calculated interaction energies and the dipole moments for the ion pairs in the gas phase were discussed.

Three-photon detachment of electrons from the fluorine negative ion

Absolute three-photon detachment cross sections are calculated for the fluorine negative ion within the lowest-order perturbation theory. The Dyson equation of the atomic many-body theory is used to obtain the ground-state 2p wavefunction with correct asymptotic behaviour, corresponding to the true (experimental) binding energy. We show that in accordance with the adiabatic theory this is crucial for obtaining absolute values of the multiphoton cross sections. Comparisons with other calculations and experimental data are presented.

Phase behavior of mixtures of colloidal platelets and nonadsorbing polymers

The phase behavior of a model system of colloidal platelets and nonadsorbing polymers is studied using computer simulations and perturbation theory. The equation of state for the pure platelet reference system is obtained by Monte Carlo simulations, and the free volume fraction accessible to polymers is measured by a trial insertion method. The free volume fraction is also calculated using scaled particle theory. Subsequently, the phase diagram for platelet-polymer mixtures is calculated. For a platelet aspect ratio L/D=0.1 and a polymer to platelet size ratio d/D>0.2, we observe coexistence between two isotropic phases with different densities. For smaller polymers d/D

Calculation of gamma spectra for positron annihilation on molecules

Calculations of gamma spectra for positron annihilation for a selection of molecules, including methane and its fluoro-substitutes, ethane, propane, butane and benzene are presented. The contribution to the ?-spectra from individual molecular orbitals is obtained from electron momentum distributions calculated using the density functional theory (DFT) based B3LYP/TZVP model. For positrons thermalised to room temperature, the calculation, in its simplest form, effectively treats the positron as a plane wave and gives positron annihilation ?-spectra linewidths that are broader (30-40%) than experiment, although the main chemical trends are reproduced. The main physical reason for this is the neglect of positron repulsion from the nuclei. We show that this effect can be incorporated through momentum-dependent correction factors, determined from positron-atom calculations, e.g., many-body perturbation theory. Inclusion of these factors in the calculation gives linewidths that are in improved agreement with experiment.

Partial and total multiphoton detachment rates for H- in a perturbative B-spline-based approach

An ab initio approach has been applied to study multiphoton detachment rates for the negative hydrogen ion in the lowest nonvanishing order of perturbation theory. The approach is based on the use of B splines allowing an accurate treatment of the electronic repulsion. Total detachment rates have been determined for two- to six-photon processes as well as partial rates for detachment into the different final symmetries. It is shown that B-spline expansions can yield accurate continuum and bound-state wave functions in a very simple manner. The calculated total rates for two- and three-photon detachment are in good agreement with other perturbative calculations. For more than three-photon detachment little information has been available before now. While the total cross sections show little structure, a fair amount of structure is predicted in the partial cross sections. In the two-photon process, it is shown that the detached electrons mainly have s character. For four- and six-photon processes, the contribution from the d channel is the most important. For three- and five-photon processes p electrons dominate the electron emission spectrum. Detachment rates for s and p electrons show minima as a function of photon energy. © 1994 The American Physical Society.

yambo: An ab initio tool for excited state calculations

yambo is an ab initio code for calculating quasiparticle energies and optical properties of electronic systems within the framework of many-body perturbation theory and time-dependent density functional theory. Quasiparticle energies are calculated within the GW approximation for the self-energy. Optical properties are evaluated either by solving the Bethe-Salpeter equation or by using the adiabatic local density approximation. yambo is a plane-wave code that, although particularly suited for calculations of periodic bulk systems, has been applied to a large variety of physical systems. yambo relies on efficient numerical techniques devised to treat systems with reduced dimensionality, or with a large number of degrees of freedom. The code has a user-friendly command-line based interface, flexible 110 procedures and is interfaced to several publicly available density functional ground-state codes.